Bound performance models of heterogeneous parallel processing systems

Systems of heterogeneous parallel processing are studied such as arising in parallel programs executed on distributed systems. A lower and an upper bound model are suggested to obtain secure lower and upper bounds on the performance of these systems. The bounding models are solved by using a matrix-geometric algorithmic approach. Formal proofs of the bounds are provided along with error bounds on the accuracy of the bounds. These error bounds in turn are reduced to simple computational expressions. Numerical results are included. The results are of interest for application to arbitrary fork-join models with parallel heterogeneous processors and synchronization